#pragma once

#include <array>
#include <concepts>
#include <cstdint>
#include <cstring>

#include "glaze/util/itoa.hpp"

#if defined(_M_X64) || defined(_M_ARM64)
#include <intrin.h>
#endif

namespace glz
{
   // Source: https://github.com/ibireme/yyjson/blob/master/src/yyjson.c

   /** Multiplies two 64-bit unsigned integers (a * b),
       returns the 128-bit result as 'hi' and 'lo'. */
   GLZ_ALWAYS_INLINE void u128_mul(uint64_t a, uint64_t b, uint64_t* hi, uint64_t* lo) noexcept
   {
#ifdef __SIZEOF_INT128__
#if defined(__GNUC__) || defined(__GNUG__)
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wpedantic"
#endif
      unsigned __int128 m = static_cast<unsigned __int128>(a) * b;
#if defined(__GNUC__) || defined(__GNUG__)
#pragma GCC diagnostic pop
#endif
      *hi = uint64_t(m >> 64);
      *lo = uint64_t(m);
#elif defined(_M_X64)
      *lo = _umul128(a, b, hi);
#elif defined(_M_ARM64)
      *hi = __umulh(a, b);
      *lo = a * b;
#else
      uint32_t a0 = (uint32_t)(a), a1 = (uint32_t)(a >> 32);
      uint32_t b0 = (uint32_t)(b), b1 = (uint32_t)(b >> 32);
      uint64_t p00 = (uint64_t)a0 * b0, p01 = (uint64_t)a0 * b1;
      uint64_t p10 = (uint64_t)a1 * b0, p11 = (uint64_t)a1 * b1;
      uint64_t m0 = p01 + (p00 >> 32);
      uint32_t m00 = (uint32_t)(m0), m01 = (uint32_t)(m0 >> 32);
      uint64_t m1 = p10 + m00;
      uint32_t m10 = (uint32_t)(m1), m11 = (uint32_t)(m1 >> 32);
      *hi = p11 + m01 + m11;
      *lo = ((uint64_t)m10 << 32) | (uint32_t)p00;
#endif
   }

   /** Multiplies two 64-bit unsigned integers and add a value (a * b + c),
       returns the 128-bit result as 'hi' and 'lo'. */
   GLZ_ALWAYS_INLINE void u128_mul_add(uint64_t a, uint64_t b, uint64_t c, uint64_t* hi, uint64_t* lo) noexcept
   {
#ifdef __SIZEOF_INT128__
#if defined(__GNUC__) || defined(__GNUG__)
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wpedantic"
#endif
      unsigned __int128 m = static_cast<unsigned __int128>(a) * b + c;
#if defined(__GNUC__) || defined(__GNUG__)
#pragma GCC diagnostic pop
#endif
      *hi = uint64_t(m >> 64);
      *lo = uint64_t(m);
#else
      uint64_t h, l, t;
      u128_mul(a, b, &h, &l);
      t = l + c;
      h += ((t < l) | (t < c));
      *hi = h;
      *lo = t;
#endif
   }

   /** Multiplies 128-bit integer and returns highest 64-bit rounded value. */
   GLZ_ALWAYS_INLINE uint64_t round_to_odd(uint64_t hi, uint64_t lo, uint64_t cp) noexcept
   {
      uint64_t x_hi, x_lo, y_hi, y_lo;
      u128_mul(cp, lo, &x_hi, &x_lo);
      u128_mul_add(cp, hi, x_hi, &y_hi, &y_lo);
      return y_hi | (y_lo > 1);
   }

   /*==============================================================================
    * Power10 Lookup Table
    *============================================================================*/

   /** Minimum decimal exponent in pow10_sig_table. */
   inline constexpr auto POW10_SIG_TABLE_128_MIN_EXP = -343;

   /** Maximum decimal exponent in pow10_sig_table. */
   inline constexpr auto POW10_SIG_TABLE_128_MAX_EXP = 324;

   /** Minimum exact decimal exponent in pow10_sig_table */
   inline constexpr auto POW10_SIG_TABLE_128_MIN_EXACT_EXP = 0;

   /** Maximum exact decimal exponent in pow10_sig_table */
   inline constexpr auto POW10_SIG_TABLE_128_MAX_EXACT_EXP = 55;

   // TODO: Remove duplicate table (see pow10_sig_table)
   inline constexpr std::array<uint64_t, 1336> pow10_sig_table_128 = {
      0xBF29DCABA82FDEAE, 0x7432EE873880FC33, /* ~= 10^-343 */
      0xEEF453D6923BD65A, 0x113FAA2906A13B3F, /* ~= 10^-342 */
      0x9558B4661B6565F8, 0x4AC7CA59A424C507, /* ~= 10^-341 */
      0xBAAEE17FA23EBF76, 0x5D79BCF00D2DF649, /* ~= 10^-340 */
      0xE95A99DF8ACE6F53, 0xF4D82C2C107973DC, /* ~= 10^-339 */
      0x91D8A02BB6C10594, 0x79071B9B8A4BE869, /* ~= 10^-338 */
      0xB64EC836A47146F9, 0x9748E2826CDEE284, /* ~= 10^-337 */
      0xE3E27A444D8D98B7, 0xFD1B1B2308169B25, /* ~= 10^-336 */
      0x8E6D8C6AB0787F72, 0xFE30F0F5E50E20F7, /* ~= 10^-335 */
      0xB208EF855C969F4F, 0xBDBD2D335E51A935, /* ~= 10^-334 */
      0xDE8B2B66B3BC4723, 0xAD2C788035E61382, /* ~= 10^-333 */
      0x8B16FB203055AC76, 0x4C3BCB5021AFCC31, /* ~= 10^-332 */
      0xADDCB9E83C6B1793, 0xDF4ABE242A1BBF3D, /* ~= 10^-331 */
      0xD953E8624B85DD78, 0xD71D6DAD34A2AF0D, /* ~= 10^-330 */
      0x87D4713D6F33AA6B, 0x8672648C40E5AD68, /* ~= 10^-329 */
      0xA9C98D8CCB009506, 0x680EFDAF511F18C2, /* ~= 10^-328 */
      0xD43BF0EFFDC0BA48, 0x0212BD1B2566DEF2, /* ~= 10^-327 */
      0x84A57695FE98746D, 0x014BB630F7604B57, /* ~= 10^-326 */
      0xA5CED43B7E3E9188, 0x419EA3BD35385E2D, /* ~= 10^-325 */
      0xCF42894A5DCE35EA, 0x52064CAC828675B9, /* ~= 10^-324 */
      0x818995CE7AA0E1B2, 0x7343EFEBD1940993, /* ~= 10^-323 */
      0xA1EBFB4219491A1F, 0x1014EBE6C5F90BF8, /* ~= 10^-322 */
      0xCA66FA129F9B60A6, 0xD41A26E077774EF6, /* ~= 10^-321 */
      0xFD00B897478238D0, 0x8920B098955522B4, /* ~= 10^-320 */
      0x9E20735E8CB16382, 0x55B46E5F5D5535B0, /* ~= 10^-319 */
      0xC5A890362FDDBC62, 0xEB2189F734AA831D, /* ~= 10^-318 */
      0xF712B443BBD52B7B, 0xA5E9EC7501D523E4, /* ~= 10^-317 */
      0x9A6BB0AA55653B2D, 0x47B233C92125366E, /* ~= 10^-316 */
      0xC1069CD4EABE89F8, 0x999EC0BB696E840A, /* ~= 10^-315 */
      0xF148440A256E2C76, 0xC00670EA43CA250D, /* ~= 10^-314 */
      0x96CD2A865764DBCA, 0x380406926A5E5728, /* ~= 10^-313 */
      0xBC807527ED3E12BC, 0xC605083704F5ECF2, /* ~= 10^-312 */
      0xEBA09271E88D976B, 0xF7864A44C633682E, /* ~= 10^-311 */
      0x93445B8731587EA3, 0x7AB3EE6AFBE0211D, /* ~= 10^-310 */
      0xB8157268FDAE9E4C, 0x5960EA05BAD82964, /* ~= 10^-309 */
      0xE61ACF033D1A45DF, 0x6FB92487298E33BD, /* ~= 10^-308 */
      0x8FD0C16206306BAB, 0xA5D3B6D479F8E056, /* ~= 10^-307 */
      0xB3C4F1BA87BC8696, 0x8F48A4899877186C, /* ~= 10^-306 */
      0xE0B62E2929ABA83C, 0x331ACDABFE94DE87, /* ~= 10^-305 */
      0x8C71DCD9BA0B4925, 0x9FF0C08B7F1D0B14, /* ~= 10^-304 */
      0xAF8E5410288E1B6F, 0x07ECF0AE5EE44DD9, /* ~= 10^-303 */
      0xDB71E91432B1A24A, 0xC9E82CD9F69D6150, /* ~= 10^-302 */
      0x892731AC9FAF056E, 0xBE311C083A225CD2, /* ~= 10^-301 */
      0xAB70FE17C79AC6CA, 0x6DBD630A48AAF406, /* ~= 10^-300 */
      0xD64D3D9DB981787D, 0x092CBBCCDAD5B108, /* ~= 10^-299 */
      0x85F0468293F0EB4E, 0x25BBF56008C58EA5, /* ~= 10^-298 */
      0xA76C582338ED2621, 0xAF2AF2B80AF6F24E, /* ~= 10^-297 */
      0xD1476E2C07286FAA, 0x1AF5AF660DB4AEE1, /* ~= 10^-296 */
      0x82CCA4DB847945CA, 0x50D98D9FC890ED4D, /* ~= 10^-295 */
      0xA37FCE126597973C, 0xE50FF107BAB528A0, /* ~= 10^-294 */
      0xCC5FC196FEFD7D0C, 0x1E53ED49A96272C8, /* ~= 10^-293 */
      0xFF77B1FCBEBCDC4F, 0x25E8E89C13BB0F7A, /* ~= 10^-292 */
      0x9FAACF3DF73609B1, 0x77B191618C54E9AC, /* ~= 10^-291 */
      0xC795830D75038C1D, 0xD59DF5B9EF6A2417, /* ~= 10^-290 */
      0xF97AE3D0D2446F25, 0x4B0573286B44AD1D, /* ~= 10^-289 */
      0x9BECCE62836AC577, 0x4EE367F9430AEC32, /* ~= 10^-288 */
      0xC2E801FB244576D5, 0x229C41F793CDA73F, /* ~= 10^-287 */
      0xF3A20279ED56D48A, 0x6B43527578C1110F, /* ~= 10^-286 */
      0x9845418C345644D6, 0x830A13896B78AAA9, /* ~= 10^-285 */
      0xBE5691EF416BD60C, 0x23CC986BC656D553, /* ~= 10^-284 */
      0xEDEC366B11C6CB8F, 0x2CBFBE86B7EC8AA8, /* ~= 10^-283 */
      0x94B3A202EB1C3F39, 0x7BF7D71432F3D6A9, /* ~= 10^-282 */
      0xB9E08A83A5E34F07, 0xDAF5CCD93FB0CC53, /* ~= 10^-281 */
      0xE858AD248F5C22C9, 0xD1B3400F8F9CFF68, /* ~= 10^-280 */
      0x91376C36D99995BE, 0x23100809B9C21FA1, /* ~= 10^-279 */
      0xB58547448FFFFB2D, 0xABD40A0C2832A78A, /* ~= 10^-278 */
      0xE2E69915B3FFF9F9, 0x16C90C8F323F516C, /* ~= 10^-277 */
      0x8DD01FAD907FFC3B, 0xAE3DA7D97F6792E3, /* ~= 10^-276 */
      0xB1442798F49FFB4A, 0x99CD11CFDF41779C, /* ~= 10^-275 */
      0xDD95317F31C7FA1D, 0x40405643D711D583, /* ~= 10^-274 */
      0x8A7D3EEF7F1CFC52, 0x482835EA666B2572, /* ~= 10^-273 */
      0xAD1C8EAB5EE43B66, 0xDA3243650005EECF, /* ~= 10^-272 */
      0xD863B256369D4A40, 0x90BED43E40076A82, /* ~= 10^-271 */
      0x873E4F75E2224E68, 0x5A7744A6E804A291, /* ~= 10^-270 */
      0xA90DE3535AAAE202, 0x711515D0A205CB36, /* ~= 10^-269 */
      0xD3515C2831559A83, 0x0D5A5B44CA873E03, /* ~= 10^-268 */
      0x8412D9991ED58091, 0xE858790AFE9486C2, /* ~= 10^-267 */
      0xA5178FFF668AE0B6, 0x626E974DBE39A872, /* ~= 10^-266 */
      0xCE5D73FF402D98E3, 0xFB0A3D212DC8128F, /* ~= 10^-265 */
      0x80FA687F881C7F8E, 0x7CE66634BC9D0B99, /* ~= 10^-264 */
      0xA139029F6A239F72, 0x1C1FFFC1EBC44E80, /* ~= 10^-263 */
      0xC987434744AC874E, 0xA327FFB266B56220, /* ~= 10^-262 */
      0xFBE9141915D7A922, 0x4BF1FF9F0062BAA8, /* ~= 10^-261 */
      0x9D71AC8FADA6C9B5, 0x6F773FC3603DB4A9, /* ~= 10^-260 */
      0xC4CE17B399107C22, 0xCB550FB4384D21D3, /* ~= 10^-259 */
      0xF6019DA07F549B2B, 0x7E2A53A146606A48, /* ~= 10^-258 */
      0x99C102844F94E0FB, 0x2EDA7444CBFC426D, /* ~= 10^-257 */
      0xC0314325637A1939, 0xFA911155FEFB5308, /* ~= 10^-256 */
      0xF03D93EEBC589F88, 0x793555AB7EBA27CA, /* ~= 10^-255 */
      0x96267C7535B763B5, 0x4BC1558B2F3458DE, /* ~= 10^-254 */
      0xBBB01B9283253CA2, 0x9EB1AAEDFB016F16, /* ~= 10^-253 */
      0xEA9C227723EE8BCB, 0x465E15A979C1CADC, /* ~= 10^-252 */
      0x92A1958A7675175F, 0x0BFACD89EC191EC9, /* ~= 10^-251 */
      0xB749FAED14125D36, 0xCEF980EC671F667B, /* ~= 10^-250 */
      0xE51C79A85916F484, 0x82B7E12780E7401A, /* ~= 10^-249 */
      0x8F31CC0937AE58D2, 0xD1B2ECB8B0908810, /* ~= 10^-248 */
      0xB2FE3F0B8599EF07, 0x861FA7E6DCB4AA15, /* ~= 10^-247 */
      0xDFBDCECE67006AC9, 0x67A791E093E1D49A, /* ~= 10^-246 */
      0x8BD6A141006042BD, 0xE0C8BB2C5C6D24E0, /* ~= 10^-245 */
      0xAECC49914078536D, 0x58FAE9F773886E18, /* ~= 10^-244 */
      0xDA7F5BF590966848, 0xAF39A475506A899E, /* ~= 10^-243 */
      0x888F99797A5E012D, 0x6D8406C952429603, /* ~= 10^-242 */
      0xAAB37FD7D8F58178, 0xC8E5087BA6D33B83, /* ~= 10^-241 */
      0xD5605FCDCF32E1D6, 0xFB1E4A9A90880A64, /* ~= 10^-240 */
      0x855C3BE0A17FCD26, 0x5CF2EEA09A55067F, /* ~= 10^-239 */
      0xA6B34AD8C9DFC06F, 0xF42FAA48C0EA481E, /* ~= 10^-238 */
      0xD0601D8EFC57B08B, 0xF13B94DAF124DA26, /* ~= 10^-237 */
      0x823C12795DB6CE57, 0x76C53D08D6B70858, /* ~= 10^-236 */
      0xA2CB1717B52481ED, 0x54768C4B0C64CA6E, /* ~= 10^-235 */
      0xCB7DDCDDA26DA268, 0xA9942F5DCF7DFD09, /* ~= 10^-234 */
      0xFE5D54150B090B02, 0xD3F93B35435D7C4C, /* ~= 10^-233 */
      0x9EFA548D26E5A6E1, 0xC47BC5014A1A6DAF, /* ~= 10^-232 */
      0xC6B8E9B0709F109A, 0x359AB6419CA1091B, /* ~= 10^-231 */
      0xF867241C8CC6D4C0, 0xC30163D203C94B62, /* ~= 10^-230 */
      0x9B407691D7FC44F8, 0x79E0DE63425DCF1D, /* ~= 10^-229 */
      0xC21094364DFB5636, 0x985915FC12F542E4, /* ~= 10^-228 */
      0xF294B943E17A2BC4, 0x3E6F5B7B17B2939D, /* ~= 10^-227 */
      0x979CF3CA6CEC5B5A, 0xA705992CEECF9C42, /* ~= 10^-226 */
      0xBD8430BD08277231, 0x50C6FF782A838353, /* ~= 10^-225 */
      0xECE53CEC4A314EBD, 0xA4F8BF5635246428, /* ~= 10^-224 */
      0x940F4613AE5ED136, 0x871B7795E136BE99, /* ~= 10^-223 */
      0xB913179899F68584, 0x28E2557B59846E3F, /* ~= 10^-222 */
      0xE757DD7EC07426E5, 0x331AEADA2FE589CF, /* ~= 10^-221 */
      0x9096EA6F3848984F, 0x3FF0D2C85DEF7621, /* ~= 10^-220 */
      0xB4BCA50B065ABE63, 0x0FED077A756B53A9, /* ~= 10^-219 */
      0xE1EBCE4DC7F16DFB, 0xD3E8495912C62894, /* ~= 10^-218 */
      0x8D3360F09CF6E4BD, 0x64712DD7ABBBD95C, /* ~= 10^-217 */
      0xB080392CC4349DEC, 0xBD8D794D96AACFB3, /* ~= 10^-216 */
      0xDCA04777F541C567, 0xECF0D7A0FC5583A0, /* ~= 10^-215 */
      0x89E42CAAF9491B60, 0xF41686C49DB57244, /* ~= 10^-214 */
      0xAC5D37D5B79B6239, 0x311C2875C522CED5, /* ~= 10^-213 */
      0xD77485CB25823AC7, 0x7D633293366B828B, /* ~= 10^-212 */
      0x86A8D39EF77164BC, 0xAE5DFF9C02033197, /* ~= 10^-211 */
      0xA8530886B54DBDEB, 0xD9F57F830283FDFC, /* ~= 10^-210 */
      0xD267CAA862A12D66, 0xD072DF63C324FD7B, /* ~= 10^-209 */
      0x8380DEA93DA4BC60, 0x4247CB9E59F71E6D, /* ~= 10^-208 */
      0xA46116538D0DEB78, 0x52D9BE85F074E608, /* ~= 10^-207 */
      0xCD795BE870516656, 0x67902E276C921F8B, /* ~= 10^-206 */
      0x806BD9714632DFF6, 0x00BA1CD8A3DB53B6, /* ~= 10^-205 */
      0xA086CFCD97BF97F3, 0x80E8A40ECCD228A4, /* ~= 10^-204 */
      0xC8A883C0FDAF7DF0, 0x6122CD128006B2CD, /* ~= 10^-203 */
      0xFAD2A4B13D1B5D6C, 0x796B805720085F81, /* ~= 10^-202 */
      0x9CC3A6EEC6311A63, 0xCBE3303674053BB0, /* ~= 10^-201 */
      0xC3F490AA77BD60FC, 0xBEDBFC4411068A9C, /* ~= 10^-200 */
      0xF4F1B4D515ACB93B, 0xEE92FB5515482D44, /* ~= 10^-199 */
      0x991711052D8BF3C5, 0x751BDD152D4D1C4A, /* ~= 10^-198 */
      0xBF5CD54678EEF0B6, 0xD262D45A78A0635D, /* ~= 10^-197 */
      0xEF340A98172AACE4, 0x86FB897116C87C34, /* ~= 10^-196 */
      0x9580869F0E7AAC0E, 0xD45D35E6AE3D4DA0, /* ~= 10^-195 */
      0xBAE0A846D2195712, 0x8974836059CCA109, /* ~= 10^-194 */
      0xE998D258869FACD7, 0x2BD1A438703FC94B, /* ~= 10^-193 */
      0x91FF83775423CC06, 0x7B6306A34627DDCF, /* ~= 10^-192 */
      0xB67F6455292CBF08, 0x1A3BC84C17B1D542, /* ~= 10^-191 */
      0xE41F3D6A7377EECA, 0x20CABA5F1D9E4A93, /* ~= 10^-190 */
      0x8E938662882AF53E, 0x547EB47B7282EE9C, /* ~= 10^-189 */
      0xB23867FB2A35B28D, 0xE99E619A4F23AA43, /* ~= 10^-188 */
      0xDEC681F9F4C31F31, 0x6405FA00E2EC94D4, /* ~= 10^-187 */
      0x8B3C113C38F9F37E, 0xDE83BC408DD3DD04, /* ~= 10^-186 */
      0xAE0B158B4738705E, 0x9624AB50B148D445, /* ~= 10^-185 */
      0xD98DDAEE19068C76, 0x3BADD624DD9B0957, /* ~= 10^-184 */
      0x87F8A8D4CFA417C9, 0xE54CA5D70A80E5D6, /* ~= 10^-183 */
      0xA9F6D30A038D1DBC, 0x5E9FCF4CCD211F4C, /* ~= 10^-182 */
      0xD47487CC8470652B, 0x7647C3200069671F, /* ~= 10^-181 */
      0x84C8D4DFD2C63F3B, 0x29ECD9F40041E073, /* ~= 10^-180 */
      0xA5FB0A17C777CF09, 0xF468107100525890, /* ~= 10^-179 */
      0xCF79CC9DB955C2CC, 0x7182148D4066EEB4, /* ~= 10^-178 */
      0x81AC1FE293D599BF, 0xC6F14CD848405530, /* ~= 10^-177 */
      0xA21727DB38CB002F, 0xB8ADA00E5A506A7C, /* ~= 10^-176 */
      0xCA9CF1D206FDC03B, 0xA6D90811F0E4851C, /* ~= 10^-175 */
      0xFD442E4688BD304A, 0x908F4A166D1DA663, /* ~= 10^-174 */
      0x9E4A9CEC15763E2E, 0x9A598E4E043287FE, /* ~= 10^-173 */
      0xC5DD44271AD3CDBA, 0x40EFF1E1853F29FD, /* ~= 10^-172 */
      0xF7549530E188C128, 0xD12BEE59E68EF47C, /* ~= 10^-171 */
      0x9A94DD3E8CF578B9, 0x82BB74F8301958CE, /* ~= 10^-170 */
      0xC13A148E3032D6E7, 0xE36A52363C1FAF01, /* ~= 10^-169 */
      0xF18899B1BC3F8CA1, 0xDC44E6C3CB279AC1, /* ~= 10^-168 */
      0x96F5600F15A7B7E5, 0x29AB103A5EF8C0B9, /* ~= 10^-167 */
      0xBCB2B812DB11A5DE, 0x7415D448F6B6F0E7, /* ~= 10^-166 */
      0xEBDF661791D60F56, 0x111B495B3464AD21, /* ~= 10^-165 */
      0x936B9FCEBB25C995, 0xCAB10DD900BEEC34, /* ~= 10^-164 */
      0xB84687C269EF3BFB, 0x3D5D514F40EEA742, /* ~= 10^-163 */
      0xE65829B3046B0AFA, 0x0CB4A5A3112A5112, /* ~= 10^-162 */
      0x8FF71A0FE2C2E6DC, 0x47F0E785EABA72AB, /* ~= 10^-161 */
      0xB3F4E093DB73A093, 0x59ED216765690F56, /* ~= 10^-160 */
      0xE0F218B8D25088B8, 0x306869C13EC3532C, /* ~= 10^-159 */
      0x8C974F7383725573, 0x1E414218C73A13FB, /* ~= 10^-158 */
      0xAFBD2350644EEACF, 0xE5D1929EF90898FA, /* ~= 10^-157 */
      0xDBAC6C247D62A583, 0xDF45F746B74ABF39, /* ~= 10^-156 */
      0x894BC396CE5DA772, 0x6B8BBA8C328EB783, /* ~= 10^-155 */
      0xAB9EB47C81F5114F, 0x066EA92F3F326564, /* ~= 10^-154 */
      0xD686619BA27255A2, 0xC80A537B0EFEFEBD, /* ~= 10^-153 */
      0x8613FD0145877585, 0xBD06742CE95F5F36, /* ~= 10^-152 */
      0xA798FC4196E952E7, 0x2C48113823B73704, /* ~= 10^-151 */
      0xD17F3B51FCA3A7A0, 0xF75A15862CA504C5, /* ~= 10^-150 */
      0x82EF85133DE648C4, 0x9A984D73DBE722FB, /* ~= 10^-149 */
      0xA3AB66580D5FDAF5, 0xC13E60D0D2E0EBBA, /* ~= 10^-148 */
      0xCC963FEE10B7D1B3, 0x318DF905079926A8, /* ~= 10^-147 */
      0xFFBBCFE994E5C61F, 0xFDF17746497F7052, /* ~= 10^-146 */
      0x9FD561F1FD0F9BD3, 0xFEB6EA8BEDEFA633, /* ~= 10^-145 */
      0xC7CABA6E7C5382C8, 0xFE64A52EE96B8FC0, /* ~= 10^-144 */
      0xF9BD690A1B68637B, 0x3DFDCE7AA3C673B0, /* ~= 10^-143 */
      0x9C1661A651213E2D, 0x06BEA10CA65C084E, /* ~= 10^-142 */
      0xC31BFA0FE5698DB8, 0x486E494FCFF30A62, /* ~= 10^-141 */
      0xF3E2F893DEC3F126, 0x5A89DBA3C3EFCCFA, /* ~= 10^-140 */
      0x986DDB5C6B3A76B7, 0xF89629465A75E01C, /* ~= 10^-139 */
      0xBE89523386091465, 0xF6BBB397F1135823, /* ~= 10^-138 */
      0xEE2BA6C0678B597F, 0x746AA07DED582E2C, /* ~= 10^-137 */
      0x94DB483840B717EF, 0xA8C2A44EB4571CDC, /* ~= 10^-136 */
      0xBA121A4650E4DDEB, 0x92F34D62616CE413, /* ~= 10^-135 */
      0xE896A0D7E51E1566, 0x77B020BAF9C81D17, /* ~= 10^-134 */
      0x915E2486EF32CD60, 0x0ACE1474DC1D122E, /* ~= 10^-133 */
      0xB5B5ADA8AAFF80B8, 0x0D819992132456BA, /* ~= 10^-132 */
      0xE3231912D5BF60E6, 0x10E1FFF697ED6C69, /* ~= 10^-131 */
      0x8DF5EFABC5979C8F, 0xCA8D3FFA1EF463C1, /* ~= 10^-130 */
      0xB1736B96B6FD83B3, 0xBD308FF8A6B17CB2, /* ~= 10^-129 */
      0xDDD0467C64BCE4A0, 0xAC7CB3F6D05DDBDE, /* ~= 10^-128 */
      0x8AA22C0DBEF60EE4, 0x6BCDF07A423AA96B, /* ~= 10^-127 */
      0xAD4AB7112EB3929D, 0x86C16C98D2C953C6, /* ~= 10^-126 */
      0xD89D64D57A607744, 0xE871C7BF077BA8B7, /* ~= 10^-125 */
      0x87625F056C7C4A8B, 0x11471CD764AD4972, /* ~= 10^-124 */
      0xA93AF6C6C79B5D2D, 0xD598E40D3DD89BCF, /* ~= 10^-123 */
      0xD389B47879823479, 0x4AFF1D108D4EC2C3, /* ~= 10^-122 */
      0x843610CB4BF160CB, 0xCEDF722A585139BA, /* ~= 10^-121 */
      0xA54394FE1EEDB8FE, 0xC2974EB4EE658828, /* ~= 10^-120 */
      0xCE947A3DA6A9273E, 0x733D226229FEEA32, /* ~= 10^-119 */
      0x811CCC668829B887, 0x0806357D5A3F525F, /* ~= 10^-118 */
      0xA163FF802A3426A8, 0xCA07C2DCB0CF26F7, /* ~= 10^-117 */
      0xC9BCFF6034C13052, 0xFC89B393DD02F0B5, /* ~= 10^-116 */
      0xFC2C3F3841F17C67, 0xBBAC2078D443ACE2, /* ~= 10^-115 */
      0x9D9BA7832936EDC0, 0xD54B944B84AA4C0D, /* ~= 10^-114 */
      0xC5029163F384A931, 0x0A9E795E65D4DF11, /* ~= 10^-113 */
      0xF64335BCF065D37D, 0x4D4617B5FF4A16D5, /* ~= 10^-112 */
      0x99EA0196163FA42E, 0x504BCED1BF8E4E45, /* ~= 10^-111 */
      0xC06481FB9BCF8D39, 0xE45EC2862F71E1D6, /* ~= 10^-110 */
      0xF07DA27A82C37088, 0x5D767327BB4E5A4C, /* ~= 10^-109 */
      0x964E858C91BA2655, 0x3A6A07F8D510F86F, /* ~= 10^-108 */
      0xBBE226EFB628AFEA, 0x890489F70A55368B, /* ~= 10^-107 */
      0xEADAB0ABA3B2DBE5, 0x2B45AC74CCEA842E, /* ~= 10^-106 */
      0x92C8AE6B464FC96F, 0x3B0B8BC90012929D, /* ~= 10^-105 */
      0xB77ADA0617E3BBCB, 0x09CE6EBB40173744, /* ~= 10^-104 */
      0xE55990879DDCAABD, 0xCC420A6A101D0515, /* ~= 10^-103 */
      0x8F57FA54C2A9EAB6, 0x9FA946824A12232D, /* ~= 10^-102 */
      0xB32DF8E9F3546564, 0x47939822DC96ABF9, /* ~= 10^-101 */
      0xDFF9772470297EBD, 0x59787E2B93BC56F7, /* ~= 10^-100 */
      0x8BFBEA76C619EF36, 0x57EB4EDB3C55B65A, /* ~= 10^-99 */
      0xAEFAE51477A06B03, 0xEDE622920B6B23F1, /* ~= 10^-98 */
      0xDAB99E59958885C4, 0xE95FAB368E45ECED, /* ~= 10^-97 */
      0x88B402F7FD75539B, 0x11DBCB0218EBB414, /* ~= 10^-96 */
      0xAAE103B5FCD2A881, 0xD652BDC29F26A119, /* ~= 10^-95 */
      0xD59944A37C0752A2, 0x4BE76D3346F0495F, /* ~= 10^-94 */
      0x857FCAE62D8493A5, 0x6F70A4400C562DDB, /* ~= 10^-93 */
      0xA6DFBD9FB8E5B88E, 0xCB4CCD500F6BB952, /* ~= 10^-92 */
      0xD097AD07A71F26B2, 0x7E2000A41346A7A7, /* ~= 10^-91 */
      0x825ECC24C873782F, 0x8ED400668C0C28C8, /* ~= 10^-90 */
      0xA2F67F2DFA90563B, 0x728900802F0F32FA, /* ~= 10^-89 */
      0xCBB41EF979346BCA, 0x4F2B40A03AD2FFB9, /* ~= 10^-88 */
      0xFEA126B7D78186BC, 0xE2F610C84987BFA8, /* ~= 10^-87 */
      0x9F24B832E6B0F436, 0x0DD9CA7D2DF4D7C9, /* ~= 10^-86 */
      0xC6EDE63FA05D3143, 0x91503D1C79720DBB, /* ~= 10^-85 */
      0xF8A95FCF88747D94, 0x75A44C6397CE912A, /* ~= 10^-84 */
      0x9B69DBE1B548CE7C, 0xC986AFBE3EE11ABA, /* ~= 10^-83 */
      0xC24452DA229B021B, 0xFBE85BADCE996168, /* ~= 10^-82 */
      0xF2D56790AB41C2A2, 0xFAE27299423FB9C3, /* ~= 10^-81 */
      0x97C560BA6B0919A5, 0xDCCD879FC967D41A, /* ~= 10^-80 */
      0xBDB6B8E905CB600F, 0x5400E987BBC1C920, /* ~= 10^-79 */
      0xED246723473E3813, 0x290123E9AAB23B68, /* ~= 10^-78 */
      0x9436C0760C86E30B, 0xF9A0B6720AAF6521, /* ~= 10^-77 */
      0xB94470938FA89BCE, 0xF808E40E8D5B3E69, /* ~= 10^-76 */
      0xE7958CB87392C2C2, 0xB60B1D1230B20E04, /* ~= 10^-75 */
      0x90BD77F3483BB9B9, 0xB1C6F22B5E6F48C2, /* ~= 10^-74 */
      0xB4ECD5F01A4AA828, 0x1E38AEB6360B1AF3, /* ~= 10^-73 */
      0xE2280B6C20DD5232, 0x25C6DA63C38DE1B0, /* ~= 10^-72 */
      0x8D590723948A535F, 0x579C487E5A38AD0E, /* ~= 10^-71 */
      0xB0AF48EC79ACE837, 0x2D835A9DF0C6D851, /* ~= 10^-70 */
      0xDCDB1B2798182244, 0xF8E431456CF88E65, /* ~= 10^-69 */
      0x8A08F0F8BF0F156B, 0x1B8E9ECB641B58FF, /* ~= 10^-68 */
      0xAC8B2D36EED2DAC5, 0xE272467E3D222F3F, /* ~= 10^-67 */
      0xD7ADF884AA879177, 0x5B0ED81DCC6ABB0F, /* ~= 10^-66 */
      0x86CCBB52EA94BAEA, 0x98E947129FC2B4E9, /* ~= 10^-65 */
      0xA87FEA27A539E9A5, 0x3F2398D747B36224, /* ~= 10^-64 */
      0xD29FE4B18E88640E, 0x8EEC7F0D19A03AAD, /* ~= 10^-63 */
      0x83A3EEEEF9153E89, 0x1953CF68300424AC, /* ~= 10^-62 */
      0xA48CEAAAB75A8E2B, 0x5FA8C3423C052DD7, /* ~= 10^-61 */
      0xCDB02555653131B6, 0x3792F412CB06794D, /* ~= 10^-60 */
      0x808E17555F3EBF11, 0xE2BBD88BBEE40BD0, /* ~= 10^-59 */
      0xA0B19D2AB70E6ED6, 0x5B6ACEAEAE9D0EC4, /* ~= 10^-58 */
      0xC8DE047564D20A8B, 0xF245825A5A445275, /* ~= 10^-57 */
      0xFB158592BE068D2E, 0xEED6E2F0F0D56712, /* ~= 10^-56 */
      0x9CED737BB6C4183D, 0x55464DD69685606B, /* ~= 10^-55 */
      0xC428D05AA4751E4C, 0xAA97E14C3C26B886, /* ~= 10^-54 */
      0xF53304714D9265DF, 0xD53DD99F4B3066A8, /* ~= 10^-53 */
      0x993FE2C6D07B7FAB, 0xE546A8038EFE4029, /* ~= 10^-52 */
      0xBF8FDB78849A5F96, 0xDE98520472BDD033, /* ~= 10^-51 */
      0xEF73D256A5C0F77C, 0x963E66858F6D4440, /* ~= 10^-50 */
      0x95A8637627989AAD, 0xDDE7001379A44AA8, /* ~= 10^-49 */
      0xBB127C53B17EC159, 0x5560C018580D5D52, /* ~= 10^-48 */
      0xE9D71B689DDE71AF, 0xAAB8F01E6E10B4A6, /* ~= 10^-47 */
      0x9226712162AB070D, 0xCAB3961304CA70E8, /* ~= 10^-46 */
      0xB6B00D69BB55C8D1, 0x3D607B97C5FD0D22, /* ~= 10^-45 */
      0xE45C10C42A2B3B05, 0x8CB89A7DB77C506A, /* ~= 10^-44 */
      0x8EB98A7A9A5B04E3, 0x77F3608E92ADB242, /* ~= 10^-43 */
      0xB267ED1940F1C61C, 0x55F038B237591ED3, /* ~= 10^-42 */
      0xDF01E85F912E37A3, 0x6B6C46DEC52F6688, /* ~= 10^-41 */
      0x8B61313BBABCE2C6, 0x2323AC4B3B3DA015, /* ~= 10^-40 */
      0xAE397D8AA96C1B77, 0xABEC975E0A0D081A, /* ~= 10^-39 */
      0xD9C7DCED53C72255, 0x96E7BD358C904A21, /* ~= 10^-38 */
      0x881CEA14545C7575, 0x7E50D64177DA2E54, /* ~= 10^-37 */
      0xAA242499697392D2, 0xDDE50BD1D5D0B9E9, /* ~= 10^-36 */
      0xD4AD2DBFC3D07787, 0x955E4EC64B44E864, /* ~= 10^-35 */
      0x84EC3C97DA624AB4, 0xBD5AF13BEF0B113E, /* ~= 10^-34 */
      0xA6274BBDD0FADD61, 0xECB1AD8AEACDD58E, /* ~= 10^-33 */
      0xCFB11EAD453994BA, 0x67DE18EDA5814AF2, /* ~= 10^-32 */
      0x81CEB32C4B43FCF4, 0x80EACF948770CED7, /* ~= 10^-31 */
      0xA2425FF75E14FC31, 0xA1258379A94D028D, /* ~= 10^-30 */
      0xCAD2F7F5359A3B3E, 0x096EE45813A04330, /* ~= 10^-29 */
      0xFD87B5F28300CA0D, 0x8BCA9D6E188853FC, /* ~= 10^-28 */
      0x9E74D1B791E07E48, 0x775EA264CF55347D, /* ~= 10^-27 */
      0xC612062576589DDA, 0x95364AFE032A819D, /* ~= 10^-26 */
      0xF79687AED3EEC551, 0x3A83DDBD83F52204, /* ~= 10^-25 */
      0x9ABE14CD44753B52, 0xC4926A9672793542, /* ~= 10^-24 */
      0xC16D9A0095928A27, 0x75B7053C0F178293, /* ~= 10^-23 */
      0xF1C90080BAF72CB1, 0x5324C68B12DD6338, /* ~= 10^-22 */
      0x971DA05074DA7BEE, 0xD3F6FC16EBCA5E03, /* ~= 10^-21 */
      0xBCE5086492111AEA, 0x88F4BB1CA6BCF584, /* ~= 10^-20 */
      0xEC1E4A7DB69561A5, 0x2B31E9E3D06C32E5, /* ~= 10^-19 */
      0x9392EE8E921D5D07, 0x3AFF322E62439FCF, /* ~= 10^-18 */
      0xB877AA3236A4B449, 0x09BEFEB9FAD487C2, /* ~= 10^-17 */
      0xE69594BEC44DE15B, 0x4C2EBE687989A9B3, /* ~= 10^-16 */
      0x901D7CF73AB0ACD9, 0x0F9D37014BF60A10, /* ~= 10^-15 */
      0xB424DC35095CD80F, 0x538484C19EF38C94, /* ~= 10^-14 */
      0xE12E13424BB40E13, 0x2865A5F206B06FB9, /* ~= 10^-13 */
      0x8CBCCC096F5088CB, 0xF93F87B7442E45D3, /* ~= 10^-12 */
      0xAFEBFF0BCB24AAFE, 0xF78F69A51539D748, /* ~= 10^-11 */
      0xDBE6FECEBDEDD5BE, 0xB573440E5A884D1B, /* ~= 10^-10 */
      0x89705F4136B4A597, 0x31680A88F8953030, /* ~= 10^-9 */
      0xABCC77118461CEFC, 0xFDC20D2B36BA7C3D, /* ~= 10^-8 */
      0xD6BF94D5E57A42BC, 0x3D32907604691B4C, /* ~= 10^-7 */
      0x8637BD05AF6C69B5, 0xA63F9A49C2C1B10F, /* ~= 10^-6 */
      0xA7C5AC471B478423, 0x0FCF80DC33721D53, /* ~= 10^-5 */
      0xD1B71758E219652B, 0xD3C36113404EA4A8, /* ~= 10^-4 */
      0x83126E978D4FDF3B, 0x645A1CAC083126E9, /* ~= 10^-3 */
      0xA3D70A3D70A3D70A, 0x3D70A3D70A3D70A3, /* ~= 10^-2 */
      0xCCCCCCCCCCCCCCCC, 0xCCCCCCCCCCCCCCCC, /* ~= 10^-1 */
      0x8000000000000000, 0x0000000000000000, /* == 10^0 */
      0xA000000000000000, 0x0000000000000000, /* == 10^1 */
      0xC800000000000000, 0x0000000000000000, /* == 10^2 */
      0xFA00000000000000, 0x0000000000000000, /* == 10^3 */
      0x9C40000000000000, 0x0000000000000000, /* == 10^4 */
      0xC350000000000000, 0x0000000000000000, /* == 10^5 */
      0xF424000000000000, 0x0000000000000000, /* == 10^6 */
      0x9896800000000000, 0x0000000000000000, /* == 10^7 */
      0xBEBC200000000000, 0x0000000000000000, /* == 10^8 */
      0xEE6B280000000000, 0x0000000000000000, /* == 10^9 */
      0x9502F90000000000, 0x0000000000000000, /* == 10^10 */
      0xBA43B74000000000, 0x0000000000000000, /* == 10^11 */
      0xE8D4A51000000000, 0x0000000000000000, /* == 10^12 */
      0x9184E72A00000000, 0x0000000000000000, /* == 10^13 */
      0xB5E620F480000000, 0x0000000000000000, /* == 10^14 */
      0xE35FA931A0000000, 0x0000000000000000, /* == 10^15 */
      0x8E1BC9BF04000000, 0x0000000000000000, /* == 10^16 */
      0xB1A2BC2EC5000000, 0x0000000000000000, /* == 10^17 */
      0xDE0B6B3A76400000, 0x0000000000000000, /* == 10^18 */
      0x8AC7230489E80000, 0x0000000000000000, /* == 10^19 */
      0xAD78EBC5AC620000, 0x0000000000000000, /* == 10^20 */
      0xD8D726B7177A8000, 0x0000000000000000, /* == 10^21 */
      0x878678326EAC9000, 0x0000000000000000, /* == 10^22 */
      0xA968163F0A57B400, 0x0000000000000000, /* == 10^23 */
      0xD3C21BCECCEDA100, 0x0000000000000000, /* == 10^24 */
      0x84595161401484A0, 0x0000000000000000, /* == 10^25 */
      0xA56FA5B99019A5C8, 0x0000000000000000, /* == 10^26 */
      0xCECB8F27F4200F3A, 0x0000000000000000, /* == 10^27 */
      0x813F3978F8940984, 0x4000000000000000, /* == 10^28 */
      0xA18F07D736B90BE5, 0x5000000000000000, /* == 10^29 */
      0xC9F2C9CD04674EDE, 0xA400000000000000, /* == 10^30 */
      0xFC6F7C4045812296, 0x4D00000000000000, /* == 10^31 */
      0x9DC5ADA82B70B59D, 0xF020000000000000, /* == 10^32 */
      0xC5371912364CE305, 0x6C28000000000000, /* == 10^33 */
      0xF684DF56C3E01BC6, 0xC732000000000000, /* == 10^34 */
      0x9A130B963A6C115C, 0x3C7F400000000000, /* == 10^35 */
      0xC097CE7BC90715B3, 0x4B9F100000000000, /* == 10^36 */
      0xF0BDC21ABB48DB20, 0x1E86D40000000000, /* == 10^37 */
      0x96769950B50D88F4, 0x1314448000000000, /* == 10^38 */
      0xBC143FA4E250EB31, 0x17D955A000000000, /* == 10^39 */
      0xEB194F8E1AE525FD, 0x5DCFAB0800000000, /* == 10^40 */
      0x92EFD1B8D0CF37BE, 0x5AA1CAE500000000, /* == 10^41 */
      0xB7ABC627050305AD, 0xF14A3D9E40000000, /* == 10^42 */
      0xE596B7B0C643C719, 0x6D9CCD05D0000000, /* == 10^43 */
      0x8F7E32CE7BEA5C6F, 0xE4820023A2000000, /* == 10^44 */
      0xB35DBF821AE4F38B, 0xDDA2802C8A800000, /* == 10^45 */
      0xE0352F62A19E306E, 0xD50B2037AD200000, /* == 10^46 */
      0x8C213D9DA502DE45, 0x4526F422CC340000, /* == 10^47 */
      0xAF298D050E4395D6, 0x9670B12B7F410000, /* == 10^48 */
      0xDAF3F04651D47B4C, 0x3C0CDD765F114000, /* == 10^49 */
      0x88D8762BF324CD0F, 0xA5880A69FB6AC800, /* == 10^50 */
      0xAB0E93B6EFEE0053, 0x8EEA0D047A457A00, /* == 10^51 */
      0xD5D238A4ABE98068, 0x72A4904598D6D880, /* == 10^52 */
      0x85A36366EB71F041, 0x47A6DA2B7F864750, /* == 10^53 */
      0xA70C3C40A64E6C51, 0x999090B65F67D924, /* == 10^54 */
      0xD0CF4B50CFE20765, 0xFFF4B4E3F741CF6D, /* == 10^55 */
      0x82818F1281ED449F, 0xBFF8F10E7A8921A4, /* ~= 10^56 */
      0xA321F2D7226895C7, 0xAFF72D52192B6A0D, /* ~= 10^57 */
      0xCBEA6F8CEB02BB39, 0x9BF4F8A69F764490, /* ~= 10^58 */
      0xFEE50B7025C36A08, 0x02F236D04753D5B4, /* ~= 10^59 */
      0x9F4F2726179A2245, 0x01D762422C946590, /* ~= 10^60 */
      0xC722F0EF9D80AAD6, 0x424D3AD2B7B97EF5, /* ~= 10^61 */
      0xF8EBAD2B84E0D58B, 0xD2E0898765A7DEB2, /* ~= 10^62 */
      0x9B934C3B330C8577, 0x63CC55F49F88EB2F, /* ~= 10^63 */
      0xC2781F49FFCFA6D5, 0x3CBF6B71C76B25FB, /* ~= 10^64 */
      0xF316271C7FC3908A, 0x8BEF464E3945EF7A, /* ~= 10^65 */
      0x97EDD871CFDA3A56, 0x97758BF0E3CBB5AC, /* ~= 10^66 */
      0xBDE94E8E43D0C8EC, 0x3D52EEED1CBEA317, /* ~= 10^67 */
      0xED63A231D4C4FB27, 0x4CA7AAA863EE4BDD, /* ~= 10^68 */
      0x945E455F24FB1CF8, 0x8FE8CAA93E74EF6A, /* ~= 10^69 */
      0xB975D6B6EE39E436, 0xB3E2FD538E122B44, /* ~= 10^70 */
      0xE7D34C64A9C85D44, 0x60DBBCA87196B616, /* ~= 10^71 */
      0x90E40FBEEA1D3A4A, 0xBC8955E946FE31CD, /* ~= 10^72 */
      0xB51D13AEA4A488DD, 0x6BABAB6398BDBE41, /* ~= 10^73 */
      0xE264589A4DCDAB14, 0xC696963C7EED2DD1, /* ~= 10^74 */
      0x8D7EB76070A08AEC, 0xFC1E1DE5CF543CA2, /* ~= 10^75 */
      0xB0DE65388CC8ADA8, 0x3B25A55F43294BCB, /* ~= 10^76 */
      0xDD15FE86AFFAD912, 0x49EF0EB713F39EBE, /* ~= 10^77 */
      0x8A2DBF142DFCC7AB, 0x6E3569326C784337, /* ~= 10^78 */
      0xACB92ED9397BF996, 0x49C2C37F07965404, /* ~= 10^79 */
      0xD7E77A8F87DAF7FB, 0xDC33745EC97BE906, /* ~= 10^80 */
      0x86F0AC99B4E8DAFD, 0x69A028BB3DED71A3, /* ~= 10^81 */
      0xA8ACD7C0222311BC, 0xC40832EA0D68CE0C, /* ~= 10^82 */
      0xD2D80DB02AABD62B, 0xF50A3FA490C30190, /* ~= 10^83 */
      0x83C7088E1AAB65DB, 0x792667C6DA79E0FA, /* ~= 10^84 */
      0xA4B8CAB1A1563F52, 0x577001B891185938, /* ~= 10^85 */
      0xCDE6FD5E09ABCF26, 0xED4C0226B55E6F86, /* ~= 10^86 */
      0x80B05E5AC60B6178, 0x544F8158315B05B4, /* ~= 10^87 */
      0xA0DC75F1778E39D6, 0x696361AE3DB1C721, /* ~= 10^88 */
      0xC913936DD571C84C, 0x03BC3A19CD1E38E9, /* ~= 10^89 */
      0xFB5878494ACE3A5F, 0x04AB48A04065C723, /* ~= 10^90 */
      0x9D174B2DCEC0E47B, 0x62EB0D64283F9C76, /* ~= 10^91 */
      0xC45D1DF942711D9A, 0x3BA5D0BD324F8394, /* ~= 10^92 */
      0xF5746577930D6500, 0xCA8F44EC7EE36479, /* ~= 10^93 */
      0x9968BF6ABBE85F20, 0x7E998B13CF4E1ECB, /* ~= 10^94 */
      0xBFC2EF456AE276E8, 0x9E3FEDD8C321A67E, /* ~= 10^95 */
      0xEFB3AB16C59B14A2, 0xC5CFE94EF3EA101E, /* ~= 10^96 */
      0x95D04AEE3B80ECE5, 0xBBA1F1D158724A12, /* ~= 10^97 */
      0xBB445DA9CA61281F, 0x2A8A6E45AE8EDC97, /* ~= 10^98 */
      0xEA1575143CF97226, 0xF52D09D71A3293BD, /* ~= 10^99 */
      0x924D692CA61BE758, 0x593C2626705F9C56, /* ~= 10^100 */
      0xB6E0C377CFA2E12E, 0x6F8B2FB00C77836C, /* ~= 10^101 */
      0xE498F455C38B997A, 0x0B6DFB9C0F956447, /* ~= 10^102 */
      0x8EDF98B59A373FEC, 0x4724BD4189BD5EAC, /* ~= 10^103 */
      0xB2977EE300C50FE7, 0x58EDEC91EC2CB657, /* ~= 10^104 */
      0xDF3D5E9BC0F653E1, 0x2F2967B66737E3ED, /* ~= 10^105 */
      0x8B865B215899F46C, 0xBD79E0D20082EE74, /* ~= 10^106 */
      0xAE67F1E9AEC07187, 0xECD8590680A3AA11, /* ~= 10^107 */
      0xDA01EE641A708DE9, 0xE80E6F4820CC9495, /* ~= 10^108 */
      0x884134FE908658B2, 0x3109058D147FDCDD, /* ~= 10^109 */
      0xAA51823E34A7EEDE, 0xBD4B46F0599FD415, /* ~= 10^110 */
      0xD4E5E2CDC1D1EA96, 0x6C9E18AC7007C91A, /* ~= 10^111 */
      0x850FADC09923329E, 0x03E2CF6BC604DDB0, /* ~= 10^112 */
      0xA6539930BF6BFF45, 0x84DB8346B786151C, /* ~= 10^113 */
      0xCFE87F7CEF46FF16, 0xE612641865679A63, /* ~= 10^114 */
      0x81F14FAE158C5F6E, 0x4FCB7E8F3F60C07E, /* ~= 10^115 */
      0xA26DA3999AEF7749, 0xE3BE5E330F38F09D, /* ~= 10^116 */
      0xCB090C8001AB551C, 0x5CADF5BFD3072CC5, /* ~= 10^117 */
      0xFDCB4FA002162A63, 0x73D9732FC7C8F7F6, /* ~= 10^118 */
      0x9E9F11C4014DDA7E, 0x2867E7FDDCDD9AFA, /* ~= 10^119 */
      0xC646D63501A1511D, 0xB281E1FD541501B8, /* ~= 10^120 */
      0xF7D88BC24209A565, 0x1F225A7CA91A4226, /* ~= 10^121 */
      0x9AE757596946075F, 0x3375788DE9B06958, /* ~= 10^122 */
      0xC1A12D2FC3978937, 0x0052D6B1641C83AE, /* ~= 10^123 */
      0xF209787BB47D6B84, 0xC0678C5DBD23A49A, /* ~= 10^124 */
      0x9745EB4D50CE6332, 0xF840B7BA963646E0, /* ~= 10^125 */
      0xBD176620A501FBFF, 0xB650E5A93BC3D898, /* ~= 10^126 */
      0xEC5D3FA8CE427AFF, 0xA3E51F138AB4CEBE, /* ~= 10^127 */
      0x93BA47C980E98CDF, 0xC66F336C36B10137, /* ~= 10^128 */
      0xB8A8D9BBE123F017, 0xB80B0047445D4184, /* ~= 10^129 */
      0xE6D3102AD96CEC1D, 0xA60DC059157491E5, /* ~= 10^130 */
      0x9043EA1AC7E41392, 0x87C89837AD68DB2F, /* ~= 10^131 */
      0xB454E4A179DD1877, 0x29BABE4598C311FB, /* ~= 10^132 */
      0xE16A1DC9D8545E94, 0xF4296DD6FEF3D67A, /* ~= 10^133 */
      0x8CE2529E2734BB1D, 0x1899E4A65F58660C, /* ~= 10^134 */
      0xB01AE745B101E9E4, 0x5EC05DCFF72E7F8F, /* ~= 10^135 */
      0xDC21A1171D42645D, 0x76707543F4FA1F73, /* ~= 10^136 */
      0x899504AE72497EBA, 0x6A06494A791C53A8, /* ~= 10^137 */
      0xABFA45DA0EDBDE69, 0x0487DB9D17636892, /* ~= 10^138 */
      0xD6F8D7509292D603, 0x45A9D2845D3C42B6, /* ~= 10^139 */
      0x865B86925B9BC5C2, 0x0B8A2392BA45A9B2, /* ~= 10^140 */
      0xA7F26836F282B732, 0x8E6CAC7768D7141E, /* ~= 10^141 */
      0xD1EF0244AF2364FF, 0x3207D795430CD926, /* ~= 10^142 */
      0x8335616AED761F1F, 0x7F44E6BD49E807B8, /* ~= 10^143 */
      0xA402B9C5A8D3A6E7, 0x5F16206C9C6209A6, /* ~= 10^144 */
      0xCD036837130890A1, 0x36DBA887C37A8C0F, /* ~= 10^145 */
      0x802221226BE55A64, 0xC2494954DA2C9789, /* ~= 10^146 */
      0xA02AA96B06DEB0FD, 0xF2DB9BAA10B7BD6C, /* ~= 10^147 */
      0xC83553C5C8965D3D, 0x6F92829494E5ACC7, /* ~= 10^148 */
      0xFA42A8B73ABBF48C, 0xCB772339BA1F17F9, /* ~= 10^149 */
      0x9C69A97284B578D7, 0xFF2A760414536EFB, /* ~= 10^150 */
      0xC38413CF25E2D70D, 0xFEF5138519684ABA, /* ~= 10^151 */
      0xF46518C2EF5B8CD1, 0x7EB258665FC25D69, /* ~= 10^152 */
      0x98BF2F79D5993802, 0xEF2F773FFBD97A61, /* ~= 10^153 */
      0xBEEEFB584AFF8603, 0xAAFB550FFACFD8FA, /* ~= 10^154 */
      0xEEAABA2E5DBF6784, 0x95BA2A53F983CF38, /* ~= 10^155 */
      0x952AB45CFA97A0B2, 0xDD945A747BF26183, /* ~= 10^156 */
      0xBA756174393D88DF, 0x94F971119AEEF9E4, /* ~= 10^157 */
      0xE912B9D1478CEB17, 0x7A37CD5601AAB85D, /* ~= 10^158 */
      0x91ABB422CCB812EE, 0xAC62E055C10AB33A, /* ~= 10^159 */
      0xB616A12B7FE617AA, 0x577B986B314D6009, /* ~= 10^160 */
      0xE39C49765FDF9D94, 0xED5A7E85FDA0B80B, /* ~= 10^161 */
      0x8E41ADE9FBEBC27D, 0x14588F13BE847307, /* ~= 10^162 */
      0xB1D219647AE6B31C, 0x596EB2D8AE258FC8, /* ~= 10^163 */
      0xDE469FBD99A05FE3, 0x6FCA5F8ED9AEF3BB, /* ~= 10^164 */
      0x8AEC23D680043BEE, 0x25DE7BB9480D5854, /* ~= 10^165 */
      0xADA72CCC20054AE9, 0xAF561AA79A10AE6A, /* ~= 10^166 */
      0xD910F7FF28069DA4, 0x1B2BA1518094DA04, /* ~= 10^167 */
      0x87AA9AFF79042286, 0x90FB44D2F05D0842, /* ~= 10^168 */
      0xA99541BF57452B28, 0x353A1607AC744A53, /* ~= 10^169 */
      0xD3FA922F2D1675F2, 0x42889B8997915CE8, /* ~= 10^170 */
      0x847C9B5D7C2E09B7, 0x69956135FEBADA11, /* ~= 10^171 */
      0xA59BC234DB398C25, 0x43FAB9837E699095, /* ~= 10^172 */
      0xCF02B2C21207EF2E, 0x94F967E45E03F4BB, /* ~= 10^173 */
      0x8161AFB94B44F57D, 0x1D1BE0EEBAC278F5, /* ~= 10^174 */
      0xA1BA1BA79E1632DC, 0x6462D92A69731732, /* ~= 10^175 */
      0xCA28A291859BBF93, 0x7D7B8F7503CFDCFE, /* ~= 10^176 */
      0xFCB2CB35E702AF78, 0x5CDA735244C3D43E, /* ~= 10^177 */
      0x9DEFBF01B061ADAB, 0x3A0888136AFA64A7, /* ~= 10^178 */
      0xC56BAEC21C7A1916, 0x088AAA1845B8FDD0, /* ~= 10^179 */
      0xF6C69A72A3989F5B, 0x8AAD549E57273D45, /* ~= 10^180 */
      0x9A3C2087A63F6399, 0x36AC54E2F678864B, /* ~= 10^181 */
      0xC0CB28A98FCF3C7F, 0x84576A1BB416A7DD, /* ~= 10^182 */
      0xF0FDF2D3F3C30B9F, 0x656D44A2A11C51D5, /* ~= 10^183 */
      0x969EB7C47859E743, 0x9F644AE5A4B1B325, /* ~= 10^184 */
      0xBC4665B596706114, 0x873D5D9F0DDE1FEE, /* ~= 10^185 */
      0xEB57FF22FC0C7959, 0xA90CB506D155A7EA, /* ~= 10^186 */
      0x9316FF75DD87CBD8, 0x09A7F12442D588F2, /* ~= 10^187 */
      0xB7DCBF5354E9BECE, 0x0C11ED6D538AEB2F, /* ~= 10^188 */
      0xE5D3EF282A242E81, 0x8F1668C8A86DA5FA, /* ~= 10^189 */
      0x8FA475791A569D10, 0xF96E017D694487BC, /* ~= 10^190 */
      0xB38D92D760EC4455, 0x37C981DCC395A9AC, /* ~= 10^191 */
      0xE070F78D3927556A, 0x85BBE253F47B1417, /* ~= 10^192 */
      0x8C469AB843B89562, 0x93956D7478CCEC8E, /* ~= 10^193 */
      0xAF58416654A6BABB, 0x387AC8D1970027B2, /* ~= 10^194 */
      0xDB2E51BFE9D0696A, 0x06997B05FCC0319E, /* ~= 10^195 */
      0x88FCF317F22241E2, 0x441FECE3BDF81F03, /* ~= 10^196 */
      0xAB3C2FDDEEAAD25A, 0xD527E81CAD7626C3, /* ~= 10^197 */
      0xD60B3BD56A5586F1, 0x8A71E223D8D3B074, /* ~= 10^198 */
      0x85C7056562757456, 0xF6872D5667844E49, /* ~= 10^199 */
      0xA738C6BEBB12D16C, 0xB428F8AC016561DB, /* ~= 10^200 */
      0xD106F86E69D785C7, 0xE13336D701BEBA52, /* ~= 10^201 */
      0x82A45B450226B39C, 0xECC0024661173473, /* ~= 10^202 */
      0xA34D721642B06084, 0x27F002D7F95D0190, /* ~= 10^203 */
      0xCC20CE9BD35C78A5, 0x31EC038DF7B441F4, /* ~= 10^204 */
      0xFF290242C83396CE, 0x7E67047175A15271, /* ~= 10^205 */
      0x9F79A169BD203E41, 0x0F0062C6E984D386, /* ~= 10^206 */
      0xC75809C42C684DD1, 0x52C07B78A3E60868, /* ~= 10^207 */
      0xF92E0C3537826145, 0xA7709A56CCDF8A82, /* ~= 10^208 */
      0x9BBCC7A142B17CCB, 0x88A66076400BB691, /* ~= 10^209 */
      0xC2ABF989935DDBFE, 0x6ACFF893D00EA435, /* ~= 10^210 */
      0xF356F7EBF83552FE, 0x0583F6B8C4124D43, /* ~= 10^211 */
      0x98165AF37B2153DE, 0xC3727A337A8B704A, /* ~= 10^212 */
      0xBE1BF1B059E9A8D6, 0x744F18C0592E4C5C, /* ~= 10^213 */
      0xEDA2EE1C7064130C, 0x1162DEF06F79DF73, /* ~= 10^214 */
      0x9485D4D1C63E8BE7, 0x8ADDCB5645AC2BA8, /* ~= 10^215 */
      0xB9A74A0637CE2EE1, 0x6D953E2BD7173692, /* ~= 10^216 */
      0xE8111C87C5C1BA99, 0xC8FA8DB6CCDD0437, /* ~= 10^217 */
      0x910AB1D4DB9914A0, 0x1D9C9892400A22A2, /* ~= 10^218 */
      0xB54D5E4A127F59C8, 0x2503BEB6D00CAB4B, /* ~= 10^219 */
      0xE2A0B5DC971F303A, 0x2E44AE64840FD61D, /* ~= 10^220 */
      0x8DA471A9DE737E24, 0x5CEAECFED289E5D2, /* ~= 10^221 */
      0xB10D8E1456105DAD, 0x7425A83E872C5F47, /* ~= 10^222 */
      0xDD50F1996B947518, 0xD12F124E28F77719, /* ~= 10^223 */
      0x8A5296FFE33CC92F, 0x82BD6B70D99AAA6F, /* ~= 10^224 */
      0xACE73CBFDC0BFB7B, 0x636CC64D1001550B, /* ~= 10^225 */
      0xD8210BEFD30EFA5A, 0x3C47F7E05401AA4E, /* ~= 10^226 */
      0x8714A775E3E95C78, 0x65ACFAEC34810A71, /* ~= 10^227 */
      0xA8D9D1535CE3B396, 0x7F1839A741A14D0D, /* ~= 10^228 */
      0xD31045A8341CA07C, 0x1EDE48111209A050, /* ~= 10^229 */
      0x83EA2B892091E44D, 0x934AED0AAB460432, /* ~= 10^230 */
      0xA4E4B66B68B65D60, 0xF81DA84D5617853F, /* ~= 10^231 */
      0xCE1DE40642E3F4B9, 0x36251260AB9D668E, /* ~= 10^232 */
      0x80D2AE83E9CE78F3, 0xC1D72B7C6B426019, /* ~= 10^233 */
      0xA1075A24E4421730, 0xB24CF65B8612F81F, /* ~= 10^234 */
      0xC94930AE1D529CFC, 0xDEE033F26797B627, /* ~= 10^235 */
      0xFB9B7CD9A4A7443C, 0x169840EF017DA3B1, /* ~= 10^236 */
      0x9D412E0806E88AA5, 0x8E1F289560EE864E, /* ~= 10^237 */
      0xC491798A08A2AD4E, 0xF1A6F2BAB92A27E2, /* ~= 10^238 */
      0xF5B5D7EC8ACB58A2, 0xAE10AF696774B1DB, /* ~= 10^239 */
      0x9991A6F3D6BF1765, 0xACCA6DA1E0A8EF29, /* ~= 10^240 */
      0xBFF610B0CC6EDD3F, 0x17FD090A58D32AF3, /* ~= 10^241 */
      0xEFF394DCFF8A948E, 0xDDFC4B4CEF07F5B0, /* ~= 10^242 */
      0x95F83D0A1FB69CD9, 0x4ABDAF101564F98E, /* ~= 10^243 */
      0xBB764C4CA7A4440F, 0x9D6D1AD41ABE37F1, /* ~= 10^244 */
      0xEA53DF5FD18D5513, 0x84C86189216DC5ED, /* ~= 10^245 */
      0x92746B9BE2F8552C, 0x32FD3CF5B4E49BB4, /* ~= 10^246 */
      0xB7118682DBB66A77, 0x3FBC8C33221DC2A1, /* ~= 10^247 */
      0xE4D5E82392A40515, 0x0FABAF3FEAA5334A, /* ~= 10^248 */
      0x8F05B1163BA6832D, 0x29CB4D87F2A7400E, /* ~= 10^249 */
      0xB2C71D5BCA9023F8, 0x743E20E9EF511012, /* ~= 10^250 */
      0xDF78E4B2BD342CF6, 0x914DA9246B255416, /* ~= 10^251 */
      0x8BAB8EEFB6409C1A, 0x1AD089B6C2F7548E, /* ~= 10^252 */
      0xAE9672ABA3D0C320, 0xA184AC2473B529B1, /* ~= 10^253 */
      0xDA3C0F568CC4F3E8, 0xC9E5D72D90A2741E, /* ~= 10^254 */
      0x8865899617FB1871, 0x7E2FA67C7A658892, /* ~= 10^255 */
      0xAA7EEBFB9DF9DE8D, 0xDDBB901B98FEEAB7, /* ~= 10^256 */
      0xD51EA6FA85785631, 0x552A74227F3EA565, /* ~= 10^257 */
      0x8533285C936B35DE, 0xD53A88958F87275F, /* ~= 10^258 */
      0xA67FF273B8460356, 0x8A892ABAF368F137, /* ~= 10^259 */
      0xD01FEF10A657842C, 0x2D2B7569B0432D85, /* ~= 10^260 */
      0x8213F56A67F6B29B, 0x9C3B29620E29FC73, /* ~= 10^261 */
      0xA298F2C501F45F42, 0x8349F3BA91B47B8F, /* ~= 10^262 */
      0xCB3F2F7642717713, 0x241C70A936219A73, /* ~= 10^263 */
      0xFE0EFB53D30DD4D7, 0xED238CD383AA0110, /* ~= 10^264 */
      0x9EC95D1463E8A506, 0xF4363804324A40AA, /* ~= 10^265 */
      0xC67BB4597CE2CE48, 0xB143C6053EDCD0D5, /* ~= 10^266 */
      0xF81AA16FDC1B81DA, 0xDD94B7868E94050A, /* ~= 10^267 */
      0x9B10A4E5E9913128, 0xCA7CF2B4191C8326, /* ~= 10^268 */
      0xC1D4CE1F63F57D72, 0xFD1C2F611F63A3F0, /* ~= 10^269 */
      0xF24A01A73CF2DCCF, 0xBC633B39673C8CEC, /* ~= 10^270 */
      0x976E41088617CA01, 0xD5BE0503E085D813, /* ~= 10^271 */
      0xBD49D14AA79DBC82, 0x4B2D8644D8A74E18, /* ~= 10^272 */
      0xEC9C459D51852BA2, 0xDDF8E7D60ED1219E, /* ~= 10^273 */
      0x93E1AB8252F33B45, 0xCABB90E5C942B503, /* ~= 10^274 */
      0xB8DA1662E7B00A17, 0x3D6A751F3B936243, /* ~= 10^275 */
      0xE7109BFBA19C0C9D, 0x0CC512670A783AD4, /* ~= 10^276 */
      0x906A617D450187E2, 0x27FB2B80668B24C5, /* ~= 10^277 */
      0xB484F9DC9641E9DA, 0xB1F9F660802DEDF6, /* ~= 10^278 */
      0xE1A63853BBD26451, 0x5E7873F8A0396973, /* ~= 10^279 */
      0x8D07E33455637EB2, 0xDB0B487B6423E1E8, /* ~= 10^280 */
      0xB049DC016ABC5E5F, 0x91CE1A9A3D2CDA62, /* ~= 10^281 */
      0xDC5C5301C56B75F7, 0x7641A140CC7810FB, /* ~= 10^282 */
      0x89B9B3E11B6329BA, 0xA9E904C87FCB0A9D, /* ~= 10^283 */
      0xAC2820D9623BF429, 0x546345FA9FBDCD44, /* ~= 10^284 */
      0xD732290FBACAF133, 0xA97C177947AD4095, /* ~= 10^285 */
      0x867F59A9D4BED6C0, 0x49ED8EABCCCC485D, /* ~= 10^286 */
      0xA81F301449EE8C70, 0x5C68F256BFFF5A74, /* ~= 10^287 */
      0xD226FC195C6A2F8C, 0x73832EEC6FFF3111, /* ~= 10^288 */
      0x83585D8FD9C25DB7, 0xC831FD53C5FF7EAB, /* ~= 10^289 */
      0xA42E74F3D032F525, 0xBA3E7CA8B77F5E55, /* ~= 10^290 */
      0xCD3A1230C43FB26F, 0x28CE1BD2E55F35EB, /* ~= 10^291 */
      0x80444B5E7AA7CF85, 0x7980D163CF5B81B3, /* ~= 10^292 */
      0xA0555E361951C366, 0xD7E105BCC332621F, /* ~= 10^293 */
      0xC86AB5C39FA63440, 0x8DD9472BF3FEFAA7, /* ~= 10^294 */
      0xFA856334878FC150, 0xB14F98F6F0FEB951, /* ~= 10^295 */
      0x9C935E00D4B9D8D2, 0x6ED1BF9A569F33D3, /* ~= 10^296 */
      0xC3B8358109E84F07, 0x0A862F80EC4700C8, /* ~= 10^297 */
      0xF4A642E14C6262C8, 0xCD27BB612758C0FA, /* ~= 10^298 */
      0x98E7E9CCCFBD7DBD, 0x8038D51CB897789C, /* ~= 10^299 */
      0xBF21E44003ACDD2C, 0xE0470A63E6BD56C3, /* ~= 10^300 */
      0xEEEA5D5004981478, 0x1858CCFCE06CAC74, /* ~= 10^301 */
      0x95527A5202DF0CCB, 0x0F37801E0C43EBC8, /* ~= 10^302 */
      0xBAA718E68396CFFD, 0xD30560258F54E6BA, /* ~= 10^303 */
      0xE950DF20247C83FD, 0x47C6B82EF32A2069, /* ~= 10^304 */
      0x91D28B7416CDD27E, 0x4CDC331D57FA5441, /* ~= 10^305 */
      0xB6472E511C81471D, 0xE0133FE4ADF8E952, /* ~= 10^306 */
      0xE3D8F9E563A198E5, 0x58180FDDD97723A6, /* ~= 10^307 */
      0x8E679C2F5E44FF8F, 0x570F09EAA7EA7648, /* ~= 10^308 */
      0xB201833B35D63F73, 0x2CD2CC6551E513DA, /* ~= 10^309 */
      0xDE81E40A034BCF4F, 0xF8077F7EA65E58D1, /* ~= 10^310 */
      0x8B112E86420F6191, 0xFB04AFAF27FAF782, /* ~= 10^311 */
      0xADD57A27D29339F6, 0x79C5DB9AF1F9B563, /* ~= 10^312 */
      0xD94AD8B1C7380874, 0x18375281AE7822BC, /* ~= 10^313 */
      0x87CEC76F1C830548, 0x8F2293910D0B15B5, /* ~= 10^314 */
      0xA9C2794AE3A3C69A, 0xB2EB3875504DDB22, /* ~= 10^315 */
      0xD433179D9C8CB841, 0x5FA60692A46151EB, /* ~= 10^316 */
      0x849FEEC281D7F328, 0xDBC7C41BA6BCD333, /* ~= 10^317 */
      0xA5C7EA73224DEFF3, 0x12B9B522906C0800, /* ~= 10^318 */
      0xCF39E50FEAE16BEF, 0xD768226B34870A00, /* ~= 10^319 */
      0x81842F29F2CCE375, 0xE6A1158300D46640, /* ~= 10^320 */
      0xA1E53AF46F801C53, 0x60495AE3C1097FD0, /* ~= 10^321 */
      0xCA5E89B18B602368, 0x385BB19CB14BDFC4, /* ~= 10^322 */
      0xFCF62C1DEE382C42, 0x46729E03DD9ED7B5, /* ~= 10^323 */
      0x9E19DB92B4E31BA9, 0x6C07A2C26A8346D1 /* ~= 10^324 */
   };

   /**
    Get the cached pow10 value from pow10_sig_table.
    @param exp10 The exponent of pow(10, e). This value must in range
                 POW10_SIG_TABLE_MIN_EXP to POW10_SIG_TABLE_MAX_EXP.
    @param hi    The highest 64 bits of pow(10, e).
    @param lo    The lower 64 bits after `hi`.
    */
   /*inline void pow10_table_get_sig_128(int32_t exp10, uint64_t *hi, uint64_t *lo) noexcept
   {
      const int32_t idx = exp10 - (POW10_SIG_TABLE_128_MIN_EXP);
      *hi = pow10_sig_table_128[idx * 2];
      *lo = pow10_sig_table_128[idx * 2 + 1];
   }*/

   inline void pow10_table_get_sig_128(const int32_t exp10, uint64_t hilo[2]) noexcept
   {
      const int32_t idx = exp10 - (POW10_SIG_TABLE_128_MIN_EXP);
      std::memcpy(hilo, pow10_sig_table_128.data() + idx * 2, 16);
   }

   /**
    Convert double number from binary to decimal.
    The output significand is shortest decimal but may have trailing zeros.

    This function use the Schubfach algorithm:
    Raffaello Giulietti, The Schubfach way to render doubles, 2020.
    https://drive.google.com/open?id=1luHhyQF9zKlM8yJ1nebU0OgVYhfC6CBN
    https://github.com/abolz/Drachennest

    See also:
    Dragonbox: A New Floating-Point Binary-to-Decimal Conversion Algorithm, 2020.
    https://github.com/jk-jeon/dragonbox/blob/master/other_files/Dragonbox.pdf
    https://github.com/jk-jeon/dragonbox

    @param sig_raw The raw value of significand in IEEE 754 format.
    @param exp_raw The raw value of exponent in IEEE 754 format.
    @param sig_bin The decoded value of significand in binary.
    @param exp_bin The decoded value of exponent in binary.
    @param sig_dec The output value of significand in decimal.
    @param exp_dec The output value of exponent in decimal.
    @warning The input double number should not be 0, inf, nan.
    */
   inline void f64_bin_to_dec(uint64_t sig_raw, int32_t exp_raw, uint64_t sig_bin, int32_t exp_bin, uint64_t* sig_dec,
                              int32_t* exp_dec) noexcept
   {
      uint64_t sp, mid;

      const bool is_even = !(sig_bin & 1);
      const bool lower_bound_closer = (sig_raw == 0 && exp_raw > 1);

      const uint64_t cb = 4 * sig_bin;
      const uint64_t cbl = cb - 2 + lower_bound_closer;
      const uint64_t cbr = cb + 2;

      /* exp_bin: [-1074, 971]                                                  */
      /* k = lower_bound_closer ? floor(log10(pow(2, exp_bin)))                 */
      /*                        : floor(log10(pow(2, exp_bin) * 3.0 / 4.0))     */
      /*   = lower_bound_closer ? floor(exp_bin * log10(2))                     */
      /*                        : floor(exp_bin * log10(2) + log10(3.0 / 4.0))  */
      const int32_t k = (exp_bin * 315653 - (lower_bound_closer ? 131237 : 0)) >> 20;

      /* k: [-324, 292]                                                         */
      /* h = exp_bin + floor(log2(pow(10, e)))                                  */
      /*   = exp_bin + floor(log2(10) * e)                                      */
      const int32_t exp10 = -k;
      const int32_t h = exp_bin + ((exp10 * 217707) >> 16) + 1;

      uint64_t pow10hilo[2];
      pow10_table_get_sig_128(exp10, pow10hilo);
      const uint64_t& pow10hi = pow10hilo[0];
      uint64_t& pow10lo = pow10hilo[1];
      pow10lo += (exp10 < POW10_SIG_TABLE_128_MIN_EXACT_EXP || exp10 > POW10_SIG_TABLE_128_MAX_EXACT_EXP);
      const uint64_t vbl = round_to_odd(pow10hi, pow10lo, cbl << h);
      const uint64_t vb = round_to_odd(pow10hi, pow10lo, cb << h);
      const uint64_t vbr = round_to_odd(pow10hi, pow10lo, cbr << h);

      const uint64_t lower = vbl + !is_even;
      const uint64_t upper = vbr - !is_even;

      bool u_inside, w_inside;

      const uint64_t s = vb / 4;
      if (s >= 10) {
         sp = s / 10;
         u_inside = (lower <= 40 * sp);
         w_inside = (upper >= 40 * sp + 40);
         if (u_inside != w_inside) {
            *sig_dec = sp + w_inside;
            *exp_dec = k + 1;
            return;
         }
      }

      u_inside = (lower <= 4 * s);
      w_inside = (upper >= 4 * s + 4);

      mid = 4 * s + 2;
      const bool round_up = (vb > mid) || (vb == mid && (s & 1) != 0);

      *sig_dec = s + ((u_inside != w_inside) ? w_inside : round_up);
      *exp_dec = k;
   }

   /** Trailing zero count table for number 0 to 99.
    (generate with misc/make_tables.c) */
   inline constexpr uint8_t dec_trailing_zero_table[] = {
      2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0};

   /**
    Write an unsigned integer with a length of 15 to 17 with trailing zero trimmed.
    These digits are named as "aabbccddeeffgghhii" here.
    For example, input 1234567890123000, output "1234567890123".
    */
   inline char* write_u64_len_15_to_17_trim(char* buf, uint64_t sig) noexcept
   {
      uint32_t tz1, tz2, tz; /* trailing zero */

      uint32_t abbccddee = uint32_t(sig / 100000000);
      uint32_t ffgghhii = uint32_t(sig - uint64_t(abbccddee) * 100000000);
      uint32_t abbcc = abbccddee / 10000; /* (abbccddee / 10000) */
      uint32_t ddee = abbccddee - abbcc * 10000; /* (abbccddee % 10000) */
      uint32_t abb = uint32_t((uint64_t(abbcc) * 167773) >> 24); /* (abbcc / 100) */
      uint32_t a = (abb * 41) >> 12; /* (abb / 100) */
      uint32_t bb = abb - a * 100; /* (abb % 100) */
      uint32_t cc = abbcc - abb * 100; /* (abbcc % 100) */

      /* write abbcc */
      buf[0] = uint8_t(a + '0');
      buf += a > 0;
      bool lz = bb < 10 && a == 0; /* leading zero */
      std::memcpy(buf, char_table + (bb * 2 + lz), 2);
      buf -= lz;
      std::memcpy(buf + 2, char_table + 2 * cc, 2);

      if (ffgghhii) {
         uint32_t dd = (ddee * 5243) >> 19; /* (ddee / 100) */
         uint32_t ee = ddee - dd * 100; /* (ddee % 100) */
         uint32_t ffgg = uint32_t((uint64_t(ffgghhii) * 109951163) >> 40); /* (val / 10000) */
         uint32_t hhii = ffgghhii - ffgg * 10000; /* (val % 10000) */
         uint32_t ff = (ffgg * 5243) >> 19; /* (aabb / 100) */
         uint32_t gg = ffgg - ff * 100; /* (aabb % 100) */
         //((uint16_t *)buf)[2] = ((const uint16_t *)char_table)[dd];
         std::memcpy(buf + 4, char_table + 2 * dd, 2);
         //((uint16_t *)buf)[3] = ((const uint16_t *)char_table)[ee];
         std::memcpy(buf + 6, char_table + 2 * ee, 2);
         //((uint16_t *)buf)[4] = ((const uint16_t *)char_table)[ff];
         std::memcpy(buf + 8, char_table + 2 * ff, 2);
         //((uint16_t *)buf)[5] = ((const uint16_t *)char_table)[gg];
         std::memcpy(buf + 10, char_table + 2 * gg, 2);
         if (hhii) {
            uint32_t hh = (hhii * 5243) >> 19; /* (ccdd / 100) */
            uint32_t ii = hhii - hh * 100; /* (ccdd % 100) */
            //((uint16_t *)buf)[6] = ((const uint16_t *)char_table)[hh];
            std::memcpy(buf + 12, char_table + 2 * hh, 2);
            //((uint16_t *)buf)[7] = ((const uint16_t *)char_table)[ii];
            std::memcpy(buf + 14, char_table + 2 * ii, 2);
            tz1 = dec_trailing_zero_table[hh];
            tz2 = dec_trailing_zero_table[ii];
            tz = ii ? tz2 : (tz1 + 2);
            buf += 16 - tz;
            return buf;
         }
         else {
            tz1 = dec_trailing_zero_table[ff];
            tz2 = dec_trailing_zero_table[gg];
            tz = gg ? tz2 : (tz1 + 2);
            buf += 12 - tz;
            return buf;
         }
      }
      else {
         if (ddee) {
            uint32_t dd = (ddee * 5243) >> 19; /* (ddee / 100) */
            uint32_t ee = ddee - dd * 100; /* (ddee % 100) */
            //((uint16_t *)buf)[2] = ((const uint16_t *)char_table)[dd];
            std::memcpy(buf + 4, char_table + 2 * dd, 2);
            //((uint16_t *)buf)[3] = ((const uint16_t *)char_table)[ee];
            std::memcpy(buf + 6, char_table + 2 * ee, 2);
            tz1 = dec_trailing_zero_table[dd];
            tz2 = dec_trailing_zero_table[ee];
            tz = ee ? tz2 : (tz1 + 2);
            buf += 8 - tz;
            return buf;
         }
         else {
            tz1 = dec_trailing_zero_table[bb];
            tz2 = dec_trailing_zero_table[cc];
            tz = cc ? tz2 : (tz1 + tz2);
            buf += 4 - tz;
            return buf;
         }
      }
   }

   consteval uint32_t numbits(uint32_t x) noexcept { return x < 2 ? x : 1 + numbits(x >> 1); }

   template <std::floating_point T>
   inline char* to_chars(char* buffer, T val) noexcept
   {
      static_assert(std::numeric_limits<T>::is_iec559);
      static_assert(std::numeric_limits<T>::radix == 2);
      static_assert(std::is_same_v<float, T> || std::is_same_v<double, T>);
      static_assert(sizeof(float) == 4 && sizeof(double) == 8);
      using raw_t = std::conditional_t<std::is_same_v<float, T>, uint32_t, uint64_t>;

      raw_t raw;
      std::memcpy(&raw, &val, sizeof(T));

      /* decode from raw bytes from IEEE-754 double format. */
      constexpr uint32_t exponent_bits =
         numbits(std::numeric_limits<T>::max_exponent - std::numeric_limits<T>::min_exponent + 1);
      constexpr raw_t sig_mask = raw_t(-1) >> (exponent_bits + 1);
      bool sign = (raw >> (sizeof(T) * 8 - 1));
      uint64_t sig_raw = raw & sig_mask;
      int32_t exp_raw = raw << 1 >> (sizeof(raw_t) * 8 - exponent_bits);

      if (exp_raw == (uint32_t(1) << exponent_bits) - 1) [[unlikely]] {
         // NaN or Infinity
         std::memcpy(buffer, "null", 4);
         return buffer + 4;
      }
      if (sign) {
         *buffer = '-';
         ++buffer;
      }
      if ((raw << 1) != 0) [[likely]] {
         uint64_t sig_bin;
         int32_t exp_bin;
         if (exp_raw == 0) [[unlikely]] {
            // subnormal
            sig_bin = sig_raw;
            exp_bin = 1 - (std::numeric_limits<T>::max_exponent - 1) - (std::numeric_limits<T>::digits - 1);
         }
         else {
            sig_bin = sig_raw | uint64_t(1ull << (std::numeric_limits<T>::digits - 1));
            exp_bin =
               int32_t(exp_raw) - (std::numeric_limits<T>::max_exponent - 1) - (std::numeric_limits<T>::digits - 1);
         }

         // if constexpr (std::same_as<T, float>) {
         //    constexpr auto shift = std::numeric_limits<double>::digits - std::numeric_limits<float>::digits;
         //    sig_bin <<= shift;
         //    exp_bin -= shift;
         // }

         /* binary to decimal */
         uint64_t sig_dec;
         int32_t exp_dec;
         f64_bin_to_dec(sig_raw, exp_raw, sig_bin, exp_bin, &sig_dec, &exp_dec);
         if constexpr (std::same_as<T, float>) {
            sig_dec *= 100000000;
            exp_dec -= 8;
         }

         int32_t sig_len = 17;
         sig_len -= (sig_dec < 100000000ull * 100000000ull);
         sig_len -= (sig_dec < 100000000ull * 10000000ull);

         /* the decimal point position relative to the first digit */
         int32_t dot_pos = sig_len + exp_dec;

         if (-6 < dot_pos && dot_pos <= 21) {
            /* no need to write exponent part */
            if (dot_pos <= 0) {
               auto num_hdr = buffer + (2 - dot_pos);
               auto num_end = write_u64_len_15_to_17_trim(num_hdr, sig_dec);
               buffer[0] = '0';
               buffer[1] = '.';
               buffer += 2;
               for (; buffer < num_hdr; ++buffer) *buffer = '0';
               return num_end;
            }
            else {
               /* dot after first digit */
               /* such as 1.234, 1234.0, 123400000000000000000.0 */
               std::memset(buffer, '0', 8);
               std::memset(buffer + 8, '0', 8);
               std::memset(buffer + 16, '0', 8);
               auto num_hdr = buffer + 1;
               auto num_end = write_u64_len_15_to_17_trim(num_hdr, sig_dec);
               for (int i = 0; i < dot_pos; i++) buffer[i] = buffer[i + 1];
               buffer[dot_pos] = '.';
               return ((num_end - num_hdr) <= dot_pos) ? buffer + dot_pos : num_end;
            }
         }
         else {
            /* write with scientific notation */
            /* such as 1.234e56 */
            auto end = write_u64_len_15_to_17_trim(buffer + 1, sig_dec);
            end -= (end == buffer + 2); /* remove '.0', e.g. 2.0e34 -> 2e34 */
            exp_dec += sig_len - 1;
            buffer[0] = buffer[1];
            buffer[1] = '.';
            end[0] = 'E';
            buffer = end + 1;
            buffer[0] = '-';
            buffer += exp_dec < 0;
            exp_dec = std::abs(exp_dec);
            if (exp_dec < 100) {
               uint32_t lz = exp_dec < 10;
               //*(uint16_t *)buffer = *(const uint16_t *)(char_table + (exp_dec * 2 + lz));
               std::memcpy(buffer, char_table + (exp_dec * 2 + lz), 2);
               return buffer + 2 - lz;
            }
            else {
               const uint32_t hi = (uint32_t(exp_dec) * 656) >> 16; /* exp / 100 */
               const uint32_t lo = uint32_t(exp_dec) - hi * 100; /* exp % 100 */
               buffer[0] = uint8_t(hi) + '0';
               std::memcpy(&buffer[1], char_table + (lo * 2), 2);
               return buffer + 3;
            }
         }
      }
      else [[unlikely]] {
         *buffer = '0';
         return buffer + 1;
      }
   }

}
